1. Field of the Invention
This invention relates to an image-processing method and, more particularly, to an image-processing method for deriving a single improved-focus two-dimensional (2-D) image of a three-dimensional (3-D) scene from a plurality of separately-focused 2-D images of this 3-D scene.
The term "scene", as used herein, means a particular region of 3-D space including all objects situated within that particular region.
2. Description of the Prior Art
As is known in optics, a pin-hole imaging system has a very deep depth-of-focus (i.e., depth-of-field), but has extremely poor light-gathering properties and poor resolution due to diffraction. Therefore, substantially all imaging is accomplished with lens imaging systems, rather than pin-hole imaging systems.
A large aperture lens (i.e., a lens having large numerical aperture and small F number) has greater light-gathering properties and is capable of providing an image of higher spatial resolution than is a small aperture lens. However, a large aperture lens inherently exhibits a relatively small depth-of-focus. For this reason, it is often not possible to produce a 2-D image of a relatively deep 3-D given scene in which both relatively close and relatively distant objects within the scene appear in good focus in the 2-D image.
The problem of insufficiency of depth-of-focus exists when a light microscope is used to examine a 3-D specimen carrying structures that extend in its depth dimension (e.g., microbiology specimens). When such a 3-D specimen is viewed in the microscope, all structures that are not in or near the focal plane are blurred or altogether invisible. One way to overcome this problem is the use of serial sectioning, a technique that involves slicing the specimen to produce a series of thin sections that may be studied individually to develop an understanding of the three-dimensional structure. However, such sectioning gives rise to other problems, such as damage or distortion of the structures carried by the specimen.
Reference is made to pages 351-360 of the book Digital Image Processing, by K. R. Castleman, published by Prentice-Hall in 1979. A three-dimensional image processing technique is described on these pages that permits a three-dimensional display to be produced by digitizing the specimen with the focal plane situated at various levels along the optical axis (equivalent to optical scanning) and then processing each resulting image to remove the defocused information from structures in neighboring planes. This approach makes it possible to roughly separate each section image into two components--a sharp component of objects in the plane of focus, and a blurred component contributed by objects lying in the other planes. By extracting the sharp components and stacking them up, a 3-D microscope scene can be displayed with a significant increase in the depth-of-field. However, this approach is only approximately correct, and it requires rather accurate a priori knowledge of the optical system parameters (i.e., optical axis positions and point spread function). Further, published photographs generated by this technique show an unnatural high-pass quality.
Reference is now made to an image-processing algorithm developed by Dr. Peter J. Burt. Dr. Burt implemented his algorithm (hereinafter referred to as the "Burt Pyramid") by computer in non-real time to effect an analysis of the two-dimensional spatial frequencies of a sampled image into a plurality of separate sets of pixel samples that define specific spatial frequency bands. Each spatial frequency band need not have a "brick wall" roll-off at given cut-off frequencies, but may have a relatively gradual roll-off because the Burt Pyramid inherently compensates for the introduction of spurious frequencies, due to aliasing, caused by a gradual roll-off. In the case of a gradual roll-off, a nominal width of a band is defined as the frequency interval between nominal cut-off frequencies at which some preselected value of attentuation in the gradual roll-off takes place. By way of example, if the highest spatial frequency of interest of the image is no greater than f.sub.0, the highest frequency band may cover an octave nominal bandwidth from f.sub.0 /2 to f.sub.0 (having a center frequency at 3f.sub.0 /4); the next-to-highest frequency band may cover an octave nominal bandwidth from f.sub.0 /4 to f.sub.0 /2 (having a center frequency at 3f.sub.0 /8), etc. Below the lowest frequency nominal bandwidth octave is a remnant band. Further, the spatial coordinates of corresponding pixel samples of all of the sample sets are the same as one another.
The following list of articles, authored or co-authored by Dr. Burt, describe in detail various aspects of the Burt pyramid:
"Segmentation and Estimation of Image Region Properties Through Cooperative Hierarchial Computation," by Peter J. Burt, et al., IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-11, No. 12, 802-809, December 1981. PA0 "The Laplacian Pyramid as a Compact Image Code," by Peter J. Burt, et al., IEEE Transactions on Communications, Vol. COM-31, No. 4, 532-540, April 1983. PA0 "Fast Algorithms for Estimating Local Image Properties," by Peter J. Burt, Computer Vision, Graphics, and Image Processing 21, 368-382 (1983). PA0 "Tree and Pyramid Structures for Coding Hexagonally Sampled Binary Images," by Peter J. Burt, Computer Graphics and Image Processing 14, 271-280 (1980). PA0 "Pyramid-based Extraction of Local Image Features with Applications to Motion and Texture Analysis," by Peter J. Burt, SPIE, Vol 360, 114-124. PA0 "Fast Filter Transforms for Image Processing," by Peter J. Burt, Computer Graphics and Image Processing 16, 20-51 (1981). PA0 "A Multiresolution Spline with Applications to Image Mosaics," by Peter J. Burt, et al., Image Processing Laboratory, Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, June 1983. PA0 "The Pyramid as a Structure for Efficient Computation," by Peter J. Burt, Image Processing Laboratory, Electrical and Systems Engineering Department, Rensselaer Polytechnic Institute, July, 1982.
Reference is further made to co-pending U.S. patent application, Ser. No. 596,817, entitled "Real-Time Hierarchal Pyramid Signal Processing Apparatus," filed Apr. 4, 1984, by Carlson, Arbeiter and Bessler, and assigned to the same assignee as the present application. This Carlson, et al. application, inter alia, discloses a two-dimensional spatial-frequency spectrum analyzer using pipe-line architecture to perform spectral analysis in delayed real time, and also discloses apparatus using pipe-line architecture fo synthesizing in delayed real time signals descriptive of the sample field analyzed by this two-dimensional spatial frequency spectrum analyzer. The analyzer and synthesizer disclosed in this co-pending Carlson, et al. patent application are capable of implementing the Burt pyramid in delayed real time.